The head of the Northern Territory health department has apologised to the families of two children who died as a result of neglect despite being known to child protection authorities.

Coroner Greg Cavanagh today found that the deaths of a baby boy in Alice Springs and a 12-year-old girl in Palmerston could have been prevented if the Territory child protection system was not "under-resourced" and "dysfunctional".

The health department's chief executive, David Ashbridge, today extended a public apology to the families.

"We let them down and it did not take the inquiries by the coroner to tell us that," he said.

"We, including myself as the chief executive of the Department of Health and Families, are sorry for what has happened.

"We cannot undo these tragedies.

"All we can do is commit the department to limiting the risk of some of these things happening again and I can assure you that we have done this and will continue to do so."